Wers. OL·XVL . )os about 9) Find Taylor ceries represenotons 003 the functions
(1) Find the Taylor series about 0 for the following functions: (a) ce (b) sin(x), (c) V1 + x (d) cos(x)
Compute the first three non-zero terms of the Taylor series for the functions: Q.1 [10 Marks] Compute the first three non-zero terms of the Taylor series for the functions: (a) (i) f(x)-In( 1 ) about a-0 where Ir < 1 (Hint: In(it)-In(1+z)-In(1-r)) (ii) From your result in (i) find ËIn(쁩) dt Page: 1 of3 MAT1841 Assignment 2 2019 Continuous Mathematics for Computer Science 3 +3+4-10 (c) h(z) = exp (sin r) about a = 픔 Q.1 [10 Marks] Compute the...
-a" (a) Find the Taylor series for sinx about x 0, and prove that it converges to sinx uniformly on any bounded interval [-N,N (b) Find the Taylor expansion of sinx about xt/6. Hence show how to annrmximate D. -a" (a) Find the Taylor series for sinx about x 0, and prove that it converges to sinx uniformly on any bounded interval [-N,N (b) Find the Taylor expansion of sinx about xt/6. Hence show how to annrmximate D.
Find the Taylor Series for the following functions at the given basepoint, and find where the series converges. None of these require making a big table (i.e. doing it the hard way)! , based at 0. (Hint: start with , replace with , then integrate term-by-term.) We were unable to transcribe this image1- We were unable to transcribe this imager2 1- r2
2. Find the Taylor series about x = 0 for x ^ 2 * cos(x ^ 2) . Also, find an expression for the general term of the series if the index starts with k = 0 0. (Hint: First find the Taylor series for cos x ^ 2 2. Find the Taylor series about x = 0 for x?cos(x?). Also, find an expression for the general term of the series if the index starts with k = 0. (Hint:...
15. (Taylor Polynomials for sin x) (a) Find the Taylor polynomials about O for f(x) = sin for n = 1,2,3,4,5,6,7,8. (b) Based on the pattern in part (a), if n is an odd number what is the relation between T. (x) and Tn+1(x)?
5. (a) (10) Write down the Taylor series for3) and find the 6th Taylor polynomial p() (b) (10) Find the Taylor series about 0 for f(a) 3 cos, and use the Lagrange Remainder Formula toshow that for any z, nlim。m(z) = 0. em t 5. (a) (10) Write down the Taylor series for3) and find the 6th Taylor polynomial p() (b) (10) Find the Taylor series about 0 for f(a) 3 cos, and use the Lagrange Remainder Formula toshow that...
(2) Show that sin(x) is the sum of its Taylor series. (3) Find the first three nonzero terms of the Taylor series about 0 for the following functions (a) cos(x2) (b) e (c) tan(x)
c,d,e please, clean work, clean handwriting please 9. Find the 10th degree Taylor polynomial for the following functions: a) cos(x2) b) sin(2x) c) ex+1 d) ex? cos(x3)
2. Find the Taylor polynomial of degree 3 (T3(x)) for each of the following functions with the specified center: (a) f(x) = er at a = 1 (b) f(x) = cos(2.r) at a = ? (c) f(x) = x2 + e + at a = -1